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arXiv · 1312.7707

Two weight norm inequalities for the bilinear fractional integrals

Kangwei Li·Wenchang Sun
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Abstract

In this paper, we give a characterization of the two weight strong and weak type norm inequalities for the bilinear fractional integrals. Namely, we give the characterization of the following inequalities, \[ \|\mathcal I_\alpha (f_1\sigma_1, f_2\sigma_2)\|_{L^q(w)} \le \mathscr N \prod_{i=1}^2\|f_i\|_{L^{p_i}(\sigma_i)} \] and \[ \|\mathcal I_\alpha (f_1\sigma_1, f_2\sigma_2)\|_{L^{q,\infty}(w)} \le \mathscr N_{\textup{weak}} \prod_{i=1}^2\|f_i\|_{L^{p_i}(\sigma_i)}, \] when $q\ge p_1, p_2>1$ and $p_1+p_2\ge p_1p_2$.

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Kangwei Li, Wenchang Sun. 2013-12-30. Two weight norm inequalities for the bilinear fractional integrals. https://arxiv.org/abs/1312.7707

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